Well the firewall is just the one built into Windows and GlassWire is just a monitoring and handling system for it so there's no "hang time". If Windows blocks something I think it's simply like there's no internet connecttion for those processes and it's all up to them if they try to reconnect from time to time or when they are meant to use the network.
Well if Butler tries to connect again when I try to log in then sure, but my first thought was that it retries if it needs to do something AND detencts that there's no connection instead of a periodical rety while there's no connection, but I'd say go with whichever is the easiest and most stable approach for the dev team. :)
Might actually try and block all the Itch connections to see what the client does. Not sure why I didn't think of that yet since it's just a flip of a button in GW.
Gonna get back to you if I tried it after work(I'm in Hungary so that'll take a few hours).